Mikele Leigertwood had put the Royals 1-0 ahead in the first half before Darius Charles equalised for the home side, but it was Shane Long's strike three minutes from time that ended Stevenage's hopes of progressing to the fifth round.
Westley said: "The lads feel very deflated back there. They have put a brilliant effort in, but we've fallen to a late goal from an excellent striker, so that's the way it goes.
"It's been a great journey. We had a terrific result in the third round against Newcastle and we all made the most of that.
"Maybe some fancied us to do the same to Reading, but Brian McDermott has got a great side and they made us work so hard straight from the off.
"They've got quality right across the park and in the end perhaps they deserved to go through to the last 16 of the competition."
Source: PA
Source: PA